We explore the role of long-range interactions in atomistic machine-learning models by analyzing the effects on fitting accuracy, isolated cluster properties, and bulk thermodynamic properties. Such models have become increasingly popular in molecular simulations given their ability to learn highly complex and multi-dimensional interactions within a local environment; however, many of them fundamentally lack a description of explicit long-range interactions. In order to provide a well-defined benchmark system with precisely known pairwise interactions, we chose as the reference model a flexible version of the Extended Simple Point Charge (SPC/E) water model. Our analysis shows that while local representations are sufficient for predictions of the condensed liquid phase, the short-range nature of machine-learning models falls short in representing cluster and vapor phase properties. These findings provide an improved understanding of the role of long-range interactions in machine learning models and the regimes where they are necessary.

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water’s solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor–liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor–liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor–liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. These results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol’s application across a large swath of water’s phase diagram.

Salt water is ubiquitous, playing crucial roles in geological and physiological processes. Despite centuries of investigations, whether or not water’s structure is drastically changed by dissolved ions is still debated. Based on density functional theory, we employ machine learning based molecular dynamics to model sodium chloride, potassium chloride, and sodium bromide solutions at different concentrations. The resulting reciprocal-space structure factors agree quantitatively with neutron diffraction data. Here we provide clear evidence that the ions in salt water do not distort the structure of water in the same way as neat water responds to elevated pressure. Rather, the computed structural changes are restricted to the ionic first solvation shells intruding into the hydrogen bond network, beyond which the oxygen radial-distribution function does not undergo major change relative to neat water. Our findings suggest that the widely cited pressure-like effect on the solvent in Hofmeister series ionic solutions should be carefully revisited.

The heats of formation and the normalized clustering energies (NCEs) for the group 4 and group 6 transition metal oxide (TMO) trimers and tetramers have been calculated by the Feller-Peterson-Dixon (FPD) method. The heats of formation predicted by the FPD method do not differ much from those previously derived from the NCEs at the CCSD(T)/aT level except for the CrO3 nanoclusters. New and improved heats of formation for Cr3O9 and Cr4O12 were obtained using PW91 orbitals instead of Hartree-Fock (HF) orbitals. Diffuse functions are necessary to predict accurate heats of formation. The fluoride affinities (FAs) are calculated with the CCSD(T) method. The relative energies (REs) of different isomers, NCEs, electron affinities (EAs), and FAs of (MO2)n (M = Ti, Zr, Hf, n = 1-4) and (MO3)n (M = Cr, Mo, W, n = 1-3) clusters have been benchmarked with 55 exchange-correlation density functional theory (DFT) functionals including both pure and hybrid types. The absolute errors of the DFT results are mostly less than ±10 kcal/mol for the NCEs and the EAs and less than ±15 kcal/mol for the FAs. Hybrid functionals usually perform better than the pure functionals for the REs and NCEs. The performance of the two types of functionals in predicting EAs and FAs is comparable. The B1B95 and PBE1PBE functionals provide reliable energetic properties for most isomers. Long range corrected pure functionals usually give poor FAs. The standard deviation of the absolute error is always close to the mean errors, and the probability distributions of the DFT errors are often not Gaussian (normal). The breadth of the distribution of errors and the maximum probability are dependent on the energy property and the isomer.

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